Potential-Based Swarm

Problem Statement

Potential-field swarm control combines attractive and repulsive fields to produce distributed collision-avoiding collective motion.

Model and Formulation

Agent force model:

$$ F_i = -\nabla U_{goal}(p_i) - \sum_{j \ne i}\nabla U_{ij}(p_i,p_j) $$

where U_{ij} can be Lennard-Jones-like or quadratic barrier potentials.

Practical Notes

• Potential shape determines spacing and rigidity.
• Local minima are a known issue in cluttered environments.
• Add damping terms to prevent oscillatory interactions.

Implementation and Execution

python -m uav_sim.simulations.swarm.potential_swarm

Evidence

References

• Spears et al., Distributed Physics-Based Control of Swarms (2004)
• Khatib, Real-Time Obstacle Avoidance for Manipulators and Mobile Robots (1986)

Related Algorithms

• Reynolds Flocking
• Voronoi Coverage